(A,B)-cyclic submodules

An (A, B)-cyclic submodule M is generated by the states of one single traje ctory of a linear control system whose parameters come from a commutative r ing. M is "finite", when it is generated by the states of a "deadbeat-contr ol" process. Motivations and basic properties of such modules are given and among several further results it is shown that the family of finite (A, B) -cyclic submodules is an invariant which (e.g., over polynomials) can be de termined by an appropriate Grobner basis computation. (C) 1999 Elsevier Sci ence Inc, All rights reserved.